Canadian Conference on Computational Chemistry
Halifax, July 19 - 24, 2009
Exploring Potential Energy Surfaces
Using Ab Initio Molecular Dynamics
Prof. H. Bernhard Schlegel
Department of Chemistry
Wayne State University
Dr. Peng Tao
Jia Zhou
Brian Psciuk
Current Research Group
Dr. Barbara Munk
Jason Sonk
Adam Birkholz
Recent Group Members
Prof. Xiaosong Li
Dr. Hrant Hratchian
Prof. Jason Sonnenberg
Dr. Stan Smith
Prof. Smriti Anand
Dr. Jie (Jessy) Li
Dr. John Knox
Michael Cato
Overview
AIMD study of non-statistical behavior
acetone radical cation and 2,4-pentanedione
radical cation dissociation
AIMD study of a Coulomb explosion:
dissociation of CH2=NHn+, (n=0,1,2,3)
Electronic response of molecules in short,
intense laser pulses
Applications of
Ab Initio Molecular Dynamics
Prof. Smriti Anand
Dr. Jie Li
Jia Zhou
Northern Virginia
Community College
Genome Center
UC Davis
Chemistry
Wayne State U.
Ab Initio Molecular Dynamics (AIMD)
 AIMD – electronic structure calculations combined with
classical trajectory calculations
 Every time the forces on the atoms in a molecule are needed,
do an electronic structure calculation
 Born – Oppenheimer (BO) method: converge the
wavefunction at each step in the trajectory
 Extended Lagrangian methods: propagate the wavefunction
along with the geometry
Car-Parrinello – plane-wave basis, propagate MO’s
ADMP – atom centered basis, propagate density matrix
Ab Initio Classical Trajectory on the
Born-Oppenheimer Surface Using Hessians
Calculate the energy,
gradient and Hessian
Millam, J. M.; Bakken, V.; Chen,
W.; Hase, W. L.; Schlegel, H. B.;
J. Chem. Phys. 1999, 111, 3800-5.
Solve the classical
equations of motion on a
local 5th order polynomial surface
Dissociation of Acetone
Radical Cation
 Dissociation of C3H6O+• has been of interest for many years now
 The enol ion is produced via the McLafferty rearrangement.
 The enol form isomerizes to the keto form, activating the newly
formed methyl group, and dissociates to form an acetyl cation
and methyl radical
 Dissociation behaves in a non-statistical manner favoring the
loss of newly formed methyl group by 1.1-1.7 to 1
Energy Dependence of the
Branching Ratio
Osterheld, T. H.; Brauman, J. I.; J. Am. Chem. Soc. 1993, 115, 10311-10316.
Potential Energy Profile (CBS-APNO)
45
+
•
CH3CO / CH3 complex
Relative Energy (kcal/mol)
35
25
15
5
Ketene/Methane complex
-5
TS for Methane Elimination
-15
Anand, S.; Schlegel, H. B. Phys. Chem. Chem. Phys. 2004, 6, 5166.
-25
Improved Potential Energy Surfaces using
Bond Additivity Corrections (BAC)
 The most important corrections needed for acetone radical cation
dissociation reaction are for C-C bond stretching potentials.
 BAC (bond additivity correction)
 add simple corrections to get better energetics for the reaction
E = E′+ ∆E
∆E = AC-C Exp{-αC-C RC-C1} + AC-C Exp{- αC-C RC-C2}
 add the corresponding corrections to gradient and hessian
G = G′+ ∂(∆E)/∂x
H = H′+ ∂2(∆E)/∂x2
 A and α are parameters obtained by fitting to high level
energies
Branching Ratios for
Microcanonical Ensemble
Initial
Branching
Energy
Ratio
(kcal/mol)
1
2
10
18
1.43
1.88
1.70
1.50
Average
Etranslation
(kcal/mol)
Average
Dissociation
Time (fs)
2.7 / 2.0
3.3 / 2.7
4.2 / 2.3
4.2 / 2.8
181 / 224
177 / 240
147 / 186
140 / 167
Effect of Adding Energy to
Specific Vibrational Modes
Energy assigned
3rd mode
0
6th mode
8th mode
1.10:1
1 kcal/mol
1.59:1
1.58:1
1.54:1
2 kcal/mol
1.84:1
2.31:1
1.82:1
4 kcal/mol
1.46:1
1.85:1
2.36:1
8 kcal/mol
1.55:1
2.03:1
2.76:1
* plus 0.5 kcal/mol in transition vector
Dissociation of Chemically Activated
Pentane-2,4-dione Radical Cation
 The enol radical cation can be produced via the McLafferty rearrangement
 Energy is localized in terminal C-C bond, but can flow to the other C-C bonds
Zhou, J.; Schlegel, H. B.; J. Phys. Chem. A 2009, 113, 1453
Potential Energy Surface for
Pentanedione Radical Cation
Number of trajectories
Kinetic Scheme for
Pentanedione Radical Cation
100
Active Acetyl
80
60
Active Methyl
40
20
Spectator Acetyl
0
0
100
200
300
400
Time (fs)
Time fs
500
600
Dissociation of Methanimine and
its Cations, CH2=NHn+ (n=0,1,2,3)
 Simplest example of a molecule with a CN double
bond, also known as methyleneimine and formaldimine
 As electrons are removed, bonding should become
weaker, finally leading to a Coulomb explosion
 CH2NH formed by pyrolysis of amines and azides, and
seen in interstellar clouds
 Monocation also well studied experimentally, but little
or no experimental information on higher cations
 Many theoretical studies over the years, but at many
different levels of theory
 Structures and energetics calculated by CBS-APNO
 Ab initio molecular dynamics by B3LYP/6-311G(d,p)
Dissociation of H2CNH
Dissociation of H2CNH+
Dissociation of H2NCH2+
Dissociation of H2NCH3+
Direct vs Indirect Dissociation
of H2CNH
Direct (no hydrogen rearrangement before dissociation)
Indirect (hydrogen migration before dissociation)
Ab Initio Molecular Dynamics
of CH2=NHn+ Dissociation
 Neutral H2CNH (200 kcal/mol initial energy)
 CH dissociation (28% direct, 4% indirect)
 NH dissociation (13% direct, 3% indirect)
 Triple dissociation (22% HCN+H+H, 9% HNC+H+H)
 Molecular dissociation (9 % HCN+H2, 10% HNC+H2)
 Monocation H2CNH+ (150 kcal/mol initial energy)
 HCNH+ + H (68% direct, 13% indirect)
 H2CN+ + H  HCNH+ + H (10%)
 Molecular dissociation (3 % HCN++H2, 3% HNC++H2)
 Dication H2NCH2+ (120 kcal/mol initial energy)
 HCNH+ + H+ (51% direct, 24% indirect)
 H2NC+ + H+ (10%)
 No reaction (13%)
Time Dependent Simulations
of Molecules in Strong Fields
Prof. Xiaosong Li
University of Washington
Jason Sonk, WSU
Prof. Robert Levis, Temple U.
Dr. Stan Smith, Temple U.
Electronic Response of Molecules
Short, Intense Laser Pulses
 For intensities of 1014 W/cm2, the electric field of the laser pulse is comparable to
Coulombic attraction felt by the valence electrons – strong field chemistry
 Need to simulate the response of the electrons to short, intense pulses
 Time dependent Schrodinger equations in terms of ground and excited states
 =  Ci(t) i
i ħ dCi(t)/dt =  Hij(t) Ci(t)
 Requires the energies of the field free states and the transition dipoles between them
 Need to limit the expansion to a subset of the excitations – TD-CIS, TD-CISD
 Time dependent Hartree-Fock equations in terms of the density matrix
i ħ dP(t)/dt = [F(t), P(t)]
 For constant F, can use a unitary transformation to integrate analytically
P(ti+1) = V  P(ti)  V† V = exp{ i t F }
 Fock matrix is time dependent because of the applied field and because of the time
dependence of the density (requires small integration step size – 0.05 au)
Hydrogen Molecule
(b)
aug-cc-pVTZ basis plus 3 sets of diffuse sp shells
Emax = 0.07 au (1.7  1014 W/cm2),  = 0.06 au (760 nm)
(a)
(c)
(b)
TD-CIS
TD-CISD
Instantaneous
dipole response
(d)
Time (0.05×au)
(c)
(e)
(f)
Fourier transform
of the residual
dipole response
Energy (au)
TD-HF
(au)
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
4
d(au)
Butadiene
Laser pulse
Dipole
2
-2
-4
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
q(au)
dx
dy
0
C1
C2
C3
C4
Charges
-2
0
2
4
6
8
10
12
14
16
18
Time (fs)
2.00
8.75×1013 W/cm2
0.25
HOMO
HOMO-1
1.95
1.90
760 nm
1.80
HF/6-31G(d,p)
0.05
1.75
0.00
0.018
2.000
0.016
HOMO-2
HOMO-3
1.996
LUMO+2
LUMO+3
0.014
0.012
1.994
0.010
n(au)
n(au)
Populations of
unoccupied orbitals
0.10
2.002
1.998
t = 0.0012 fs
0.15
Populations of
occupied orbitals
1.85
LUMO
LUMO+1
0.20
1.992
1.990
0.008
0.006
1.988
0.004
1.986
0.002
1.984
0.000
1.982
2.000
0.010
HOMO-4
HOMO-5
1.998
LUMO+4
LUMO+5
0.008
1.996
0.006
1.994
0.004
1.992
0.002
1.990
0.000
1.988
-2
0
2
4
6
8
Time (fs)
10
12
14
16
18
-2
0
2
4
6
8
Time (fs)
10
12
14
16
18
Butadiene, Hexatriene and Naphthalene
TD-CIS/6-31G(d,p),  = 0.06 au (760 nm)
Excited state weights in the final wavefunction
Excited State Energies of Butadiene
RPA
CIS
CIS(D)
CISD
EOM-CCSD
* Transition Dipoles for
Butadiene (6-31G(d,p) basis)
Response of 2 and 3 Level Systems
to a 3 Cycle Gaussian Pulse
I
0.25
0.04
0.02
0.00
2
0.02
0.04
0.35
0.25
0.00
4
6
8
fs
Response of the  States of Butadiene
to a 3 Cycle Gaussian Pulse
TD-CIS
1A
g
TD-EOMCC
(gs)
1B
u
1A
g
1B
u
TD-CIS response
vs number of states
0.02
0.01
80
100
120
Number of States
140
160
1.0
Energy (au)
 A large number of states are
needed for the response to
be stable
 Lowest states are well
separated
 Higher states form a
quasi-continuum
 Most of the higher lying
states are needed primarily
to represent the polarization
of the molecule in the field
Wavefunction Coefficient
0.03
0.8
0.6
0.4
0.2
20
40
60
State Number
80
100
TD-CIS in a Reduced Space
 Perturbation theory for the effective polarizability of the low lying states
i  2
high lying

i | r | k /(k  i )
2
k
 Finite difference method for the effective polarizability
 i  (i (e)  2i (0)  i (e)) / e2 i (e)  UT (H  D ' e)U
where D' is the matrix of transition dipoles with the elements between the low
lying states set to zero
 Integrate TD-CI equations with polarizability
i dCi (t ) dt  H ij (t ) C j (t )
H ij (t )  i  ij  2 e(t ) i e(t )  ij  Dij e(t )
1
TD-CIS in a Reduced Space
Butadiene, TD-CIS/6-31G(d,p)
Emax = 0.05 au (8.75  1013 W/cm2),  = 0.06 au (760 nm)
 Large CIS space
 Small CIS space with polarizability
3
3
2
2
Instantaneous Dipole
1
Instantaneous Dipole
1
2
4
6
8
10
12
14
16
Time (fs)
1
2
4
6
8
10
12
14
16
Time (fs)
1
2
2
3
3
0.025
0.025
0.020
0.020
Wavefunction
Coefficients
0.015
0.010
0.010
0.005
0.005
0.000
0.0
0.2
0.4
0.6
Energy (au)
0.8
1.0
Wavefunction
Coefficients
0.015
0.000
0.0
0.2
0.4
0.6
Energy (au)
0.8
1.0
Response of Butadiene
to a 3 Cycle Gaussian Pulse
(=0.6 au, 6-31G(d,p) basis)
RPA
TD-CIS
TD-CIS(D)
TD-EOMCC
Transition Dipoles for Butadiene
(CIS)
Response of Butadiene
to a 3 Cycle Gaussian Pulse
(=0.6 au, TD-CIS)
6-31G(d,p)
6-31++G(d,p)
6-311++G(2df,2pd)
Acknowledgements
Current Research Group
Dr. Peng Tao
Jia Zhou
Brian Psciuk
Collaborators:
Dr. Barbara Munk
Jason Sonk
Adam Birkholz
Recent Group Members
Prof. Jason Sonnenberg, Stevenson University,
Prof. Xiaosong Li, U. of Washington
Prof. Smriti Anand, Northern Virginia College
Dr. Hrant Hratchian, Gaussian, Inc.
Dr. Jie Li, U. California, Davis (Duan group)
Dr. Stan Smith, Temple U. (Levis group)
Dr. John Knox, GlaxoSmithKline (Singapore)
Michael Cato, Jackson State U. (Leszczynski group)
Funding and Resources:
National Science Foundation
Office of Naval Research
NIH
Gaussian, Inc.
Wayne State U.
Dr. T. Vreven, Gaussian Inc.
Dr. M. J. Frisch, Gaussian Inc.
Prof. John SantaLucia, Jr., WSU
Raviprasad Aduri (SantaLucia group)
Prof. G. Voth, U. of Utah
Prof. David Case, Scripps
Prof. Bill Miller, UC Berkeley
Prof. Thom Cheatham, U. of Utah
Prof. S.O. Mobashery, Notre Dame U.
Prof. R.J. Levis, Temple U.
Prof. C.H. Winter, WSU
Prof. C. Verani, WSU
Prof. E. M. Goldfield, WSU
Prof. D. B. Rorabacher, WSU
Prof. J. F. Endicott, WSU
Prof. J. W. Montgomery, U. of Michigan
Prof. Sason Shaik, Hebrew University
Prof. P.G. Wang, Ohio State U.
Prof. Ted Goodson, U. of Michigan
Prof. G. Scuseria, Rice Univ.
Prof. Srini Iyengar, Indiana U
Prof. O. Farkas, ELTE
Prof. M. A. Robb, Imperial, London
Recent Group Members
Current Group Members